We also consider applications to the Fermi-Hubbard model, which is believed to capture the physics of some high temperature superconductors. This model is classically challenging to simulate [1]}, [2]}, but is a potential candidate for near-term quantum simulation [3]}, [4]}, [5]}, [6]}. We have
\(H=-s \sum _{\langle j,k\rangle ,\sigma }\left(A_{j,\sigma }^\dagger A_{k,\sigma }+A_{k,\sigma }^\dagger A_{j,\sigma }\right)+v\sum _{j}N_{j,0}N_{j,1},\) 
